The present invention relates to a circuit and a method for pre-distorting an input signal to be transmitted via a power amplifier having a non-linear transmission characteristic using non-orthogonal coordinates in order to compensate for level-dependent non-linearities of the gain of the amplifier.
The present invention can be used for conducting a pretreatment of input signals formed using modulation methods which result in a non-constant envelope of the radio frequency carrier signal. Thus, the present invention preferably finds use in transmitters for digital broadcasting, which are fed by multi-carrier signals, such as OFDM signals (OFDM=orthogonal frequency division multiplex), for example. With such signals, the non-linearity of the amplifier causes unwanted frequency portions of the signal at the output of the amplifier. Such frequency portions interfer with adjacent-frequency channels.
In addition, the present invention is applicable to mobile communication systems using CDMA signals (CDMA=code division multiple access), for example. Additionally, the present invention can be advantageously used in satellite earth stations or base stations of mobile telephone systems.
A multitude of systems is known for pre-distorting the input signal to be transmitted via a RF power amplifier such that non-linear distortions caused by the output stage, i.e., the RF power amplifier, are compensated for as far as possible. The non-linear distortions are described by AM/AM and AM/PM characteristic curves in case of memory-free amplifiers. A system for performing an amplifier linearization by adaptive pre-distortion is described in U.S. Pat. No. 5,049,832.
A pre-distorter having a structure as described in U.S. Pat. No. 5,049,832 is shown in FIG. 3 of the present application. Squared magnitude values of a complex base-band signal v(k) representing the input signal to a power amplifier, are derived in a unit 10. k is a running index in the direction of the time axis for respective samples. Unit 10 derives the sum of squares of the magnitude of the real and imaginary parts of the complex base-band signal v(k), i.e., |I2+Q2|. Based on the squared magnitude values, a look-up table 12 is accessed. Each table entry of the look-up table 12 is associated with a section of squared magnitude values. Thus, section-wise constant pre-distortion coefficients are stored in the look-up table 12. The table entries for respective squared magnitude values are set to provide pre-distortion for the input signal v(k) which compensates for level-dependent non-linearities of the gain of the power amplifier (not shown in FIG. 3). For any input power, the optimum value of the complex gain of the pre-distortion, i.e., the table entries, is determined by equating the composite pre-distorter/power amplifier non-linearity to a nominal constant amplitude gain of the power amplifier.
The input signal v(k) is pre-distorted by the table entries using a pre-distorter 14. The pre-distorted input signal vxe2x80x2(k) is applied to the power amplifier. The pre-distorter 14 performs a complex multiplication of the complex input signal v(k) by the complex table entries obtained from the look-up table 12. A respective table entry is formed by a complex pre-distortion coefficient composed of a real part AR and an imaginary part AI. The complex pre-distortion coefficients are stored in the look-up table 12 in rectangular coordinates. Thus, the pre-distorted input signal vxe2x80x2(k) is obtained by pre-distorting the input signal using complex pre-distortion coefficients stored in orthogonal coordinates in the look-up table 12. A predistortion according to the following equation is performed by the pre-distorter 14 shown in FIG. 3:
vxe2x80x2(k)=v(k)xc2x7A(n)
wherein k is a running index in the time axis, and
n=f(v(k));
To be more specific:
vxe2x80x2(k)=(RE{v(k)}+jIm{v(k)})xc2x7(AR(n)+jAI(n))
The system described in U.S. Pat. No. 5,049,832 is able to conduct a pre-distortion of an input signal through the entire complex plane. Thus, theoretically, AM/AM and AM/PM distortions of any extent can be compensated for. However, as a result, a look-up table having an adequate word length has to be used.
It is the object of the present invention to provide a system for performing a pre-distortion of an input signal to be transmitted via a power amplifier, which enables usage of a look-up table having a reduced size for storing complex pre-distortion coefficients.
This object is achieved by a.circuit according to claim 1 and a method according to claim 7.
The present invention provides a circuit for pre-distorting an input signal v to be transmitted via a power amplifier having a non-linear transmission characteristic to produce a pre-distorted input signal, the circuit comprising:
an estimator for determining an estimation signal based on the power of said input signal;
a look-up table for storing complex pre-distortion coefficients BR and AI which depend on the power of said input signal and the non-linear transmission characteristic of the power amplifier determined in advance, wherein BR=ARxe2x88x92K, K being a constant with 0 less than K less than 2, and AR and AI are the real and imaginary parts of a complex pre-distortion function A which provides a pre-distortion of the input signal v such that the distortion introduced by the non-linear transmission characteristic is substantially compensated according to magnitude and phase; and
a pre-distorter for pre-distorting the input signal according to y=vxc2x7(K+BR+jAI).
The present invention is based on the recognition that it is possible to realize an adaptive pre-distortion with reduced expense. The inventors recognized that power amplifiers used in practice have typically limited phase errors and amplitude errors. For example, semiconductor output stages used in practice have a typical maximum phase error of xc2x15xc2x0 and a maximum amplitude error of approximately 2 dB. Similarily, travelling wave tubes exhibit a maximum phase error of approximately 30xc2x0 and an amplitude error of approximately 5 dB.
The fact that power amplifiers used in practice have limited phase errors and amplitude errors will make significant simplification of prior art realizations of pre-distorting systems possible. In particular, in case of realizations using field programmable gate arrays (FPGA), substantial cost savings will be obtained.
Generally, a pre-distortion of a digital complex input signal to be transmitted via a power amplifier having a non-linear transmission characteristic can be described as follows:
y(k)=v(k)xc2x7A(f(v(k)))
wherein v is the complex input signal, y is the complex pre-distorted input signal (i.e., the output signal of the pre-distorter) and A is the complex correction value for the AM/AM and AM/PM distortions of the power amplifier which depend on the amplitude of the input signal v. f is a function appropriate for determining the amplitude or the squared amplitude of the input signal v. Both the amplitude and the squared amplitude are a measure for the power of the input signal. k is a running index in the direction of the time axis indicating respective sample times. The complex correction value A is stored in the form of a table containing real and imaginary pre-distortion coefficients which are preferably adaptively obtained from a comparison of the output signal of the power amplifier and the input signal fed to the amplifier.
Now, the present invention makes use of the fact that the range of values of A is limited with respect to the magnitude of the complex correction coefficients AR and AI which build up the correction function A. Actually, power amplifier used in practice only require a pre-distortion of typically up to 5xc2x0 and 2 dB. The assumption mentioned above provides space for practical inexpensive realizations which are based on an implementation of the multiplication vxc2x7A in a non-orthogonal coordinate system, rather than in a Cartesian or polar coordinate system as it is the case in prior art solutions.
For the real part, AR of the complex pre-distortion coefficients, the following relation applies:
(1xe2x88x92a) less than AR less than (1+a).
For the imaginary part AI of the complex pre-distortion coefficients, the following equation applies:
xe2x88x92b less than AI less than B.
Thus, AR accepts values in a range adjacent to one, whereas AI accepts values in a range adjacent to zero. Having the above relations in mind, the inventors recognized that a look-up table having a reduced word length can be used in case ARxe2x88x92K is stored in the look-up table rather than AR, wherein K is a constant with 0 less than K less than 2. Due to the range of values of the real coefficient AR mentioned above, best result will be achieved in case the constant K is set to be one. However, a reduction of the word length can be achieved as long as K is chosen to be greater than 0 and not greater than 2.
Thus, BR=ARxe2x88x92K is stored as the real pre-distortion coefficients in the look-up table.
This modification of the stored real coefficient has to be compensated for in the pre-distorter which is coupled with the input signal and the look-up table. Therefore, the pre-distortion. conducted by the pre-distorter has to meet the following equation:
y(k)=(RE{v(k)}+jIm{v(k)})xc2x7(K+BR(n)+jAI(n))
wherein n=f(v(k)).
A further improvement can be achieved in case BR and AI are limited to +/xe2x88x920,125. In this case, the word length at one input of the multiplier used in the pre-distorter can be reduced by three bits. Limitating BR and AI, to the value mentioned above, maximum amplitude errors of the power amplifier up to xe2x88x922,13 dB and phase errors of xc2x17xc2x0 can be compensated for. Such a compensation is sufficient for practically used semiconductor amplifiers or klystrons, for example.
Thus, the inventors recognized that an inexpensive implementation for conducting a pre-distortion of an input signal of a power amplifier can be achieved in case the orthogonality of the complex pre-distortion values stored in the look-up table is given up.